How is prime factorization calculated?

By repeatedly dividing the number by the smallest possible prime until only prime factors remain.

Why is prime factorization useful?

It's foundational for finding GCF and LCM, and underlies cryptographic systems like RSA encryption.

Prime Factorization Calculator - CalculatorLabs.net

Q: What is prime factorization?

Breaking a number down into the set of prime numbers that multiply together to produce it.

Prime Factorization Calculator

Break any whole number down into its prime building blocks.

Number

Prime Factorization-

Distinct Prime Factors-

What Is Prime Factorization?

Prime factorization breaks a number down into the prime numbers that multiply together to make it. Every whole number greater than 1 has exactly one prime factorization — this is called the Fundamental Theorem of Arithmetic. It's the basis for simplifying fractions, finding LCM/GCF, and much of number theory.

A factor tree splits a number into primes step by step.

Method

Divide repeatedly by the smallest prime (2, 3, 5, 7, ...) until only 1 remains.

How to Use This Calculator

Enter any whole number greater than 1.
Click "Find Prime Factors".
See the full factorization written as a product of primes, plus the distinct primes involved. If the number itself is prime, that's flagged too.

Worked Example

Example: 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.